Obtain the derivative and unit tangent vector at for a vector function
We are given the vector function: \[ \vec{a}(t) = t\hat{i} + e^{t^2}\hat{j} + \sin(2t)\hat{k} \] ### Step 1: Compute the Derivative \(\vec{a}'(t)\) To find the derivative, differentiate each component with respect to \( t \): \[ \frac{d}{dt} (t) = 1 \] \[ \frac{d}{dt} (e^{t^2}) = 2t e^{t^2} \] \[ \frac{d}{dt} (\sin(2t)) = 2\cos(2t) \] Thus, ___ ________ ____ ________ ___ _________ ___ ______ __________ ___.
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Obtain the derivative and unit tangent vector at for a vector function
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